Difficulty: Easy
Correct Answer: 110 cm
Explanation:
Introduction / Context:
This is a direct application of the circumference formula for a circle. The question gives the diameter and asks for the circumference, which is an essential and very frequently tested relationship in basic geometry and aptitude.
Given Data / Assumptions:
Concept / Approach:
Circumference C of a circle can be written in two equivalent forms:
C = pi * d, or C = 2 * pi * r.
Here we are directly given the diameter, so we use C = pi * d. We substitute d = 35 cm and pi = 22 / 7 to compute C.
Step-by-Step Solution:
Step 1: Use the formula C = pi * d.
Step 2: Substitute pi = 22 / 7 and d = 35 cm.
Step 3: C = (22 / 7) * 35.
Step 4: Simplify 35 / 7 = 5.
Step 5: So C = 22 * 5 = 110 cm.
Verification / Alternative check:
We can also find the radius and then use the formula 2 * pi * r. Radius r = d / 2 = 35 / 2 = 17.5 cm. Then:
C = 2 * pi * r = 2 * (22 / 7) * 17.5.
17.5 / 7 = 2.5, so C = 2 * 22 * 2.5 = 44 * 2.5 = 110 cm. This confirms the same result using an alternate method.
Why Other Options Are Wrong:
70 cm: This would apply if pi was approximated as 2, which is incorrect.
77 cm: Equals pi * radius (22 / 7 * 17.5) only if one misapplies the formula; it does not match the correct circumference here.
140 cm: This value equals 4 * pi * r with r = 17.5 and is not the correct formula for circumference.
220 cm: Exactly double the correct answer and corresponds to using 2 * pi * d, which is wrong.
Common Pitfalls:
Learners sometimes confuse diameter with radius, mistakenly substituting 35 as the radius and using 2 * pi * r, leading to double the correct answer. Another common issue is forgetting that C = pi * d is already fully sufficient when diameter is given. Always identify whether you are given diameter or radius before picking the formula.
Final Answer:
The circumference of the circle is 110 cm.
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